Preheat broiler, and line a large baking sheet with aluminum foil.
In a large skillet set over medium-high heat, melt the butter until foamy. Add garlic and cook until fragrant, about 30 seconds. Remove from heat, and stir in artichoke hearts, mozzarella, cheddar, Parmesan, sour cream and shallot until combined.
Slice the bread lengthwise. Place the bread halves on the prepared baking sheet, cut side up, and spoon the cooled cheese and artichoke mixture overtop, add a sprinkling of chives. Broil until cheese is melted and bread is hot.Sprinkle more fresh chives over each piece.

Cut each half into six pieces and serve right away, while the cheese is still warm.